Final answer:
The correct expressions according to DeMorgan’s theorem are ~(A AND B) = ~A OR ~B and ~(A OR B) = ~A AND ~B. These rules can be applied in logic, set theory, and computer science to negate conjunctions and disjunctions.
Step-by-step explanation:
The correct expressions according to DeMorgan’s theorem are:
- ~(A AND B) = ~A OR ~B
- ~(A OR B) = ~A AND ~B
DeMorgan's theorem describes how mathematical statements and concepts are transformed through negation. When negating a conjunction (AND statement), it becomes a disjunction (OR statement) with negated operands. Conversely, when negating a disjunction (OR statement), it becomes a conjunction (AND statement) with negated operands. This theorem is important in set theory, logic, and various fields of computer science.
The correct options from the provided list are:
- A. ~(A AND B) = ~A OR ~B
- B. ~(A OR B) = ~A AND ~B
Options C and D are incorrect according to DeMorgan's theorem. Remember that the '~' symbol represents the negation ('not') operator.